From CVaR to Uncertainty Set: Implications in Joint Chance-Constrained Optimization

Authors:
Wenqing Chen;Melvyn Sim;Jie Sun;Chung-Piaw Teo
Affiliations:
NUS Business School, National University of Singapore, Singapore;NUS Business School and NUS Risk Management Institute, National University of Singapore, Singapore;NUS Business School and NUS Risk Management Institute, National University of Singapore, Singapore;NUS Business School, National University of Singapore, Singapore
Venue:
Operations Research
Year:
2010

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Abstract

We review and develop different tractable approximations to individual chance-constrained problems in robust optimization on a variety of uncertainty sets and show their interesting connections with bounds on the conditional-value-at-risk (CVaR) measure. We extend the idea to joint chance-constrained problems and provide a new formulation that improves upon the standard approach. Our approach builds on a classical worst-case bound for order statistics problems and is applicable even if the constraints are correlated. We provide an application of the model on a network resource allocation problem with uncertain demand.